Write 2^15 ÷ 2^9 in the form 2^k where k is an integer to be found

The domain of the function is positive integers. The function () = 200 + 16 represents the daily cost of production in a factory, where x is the number of complete products manufactured.

Since the production of products cannot be negative or fractional, the domain of the function is restricted to non-negative integers.

Therefore, the domain of the function is the set of positive integers:

{1, 2, 3, 4, ...}

Any value outside this set would not make sense in the context of the problem, as a fraction or a negative number of products cannot be produced.

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The calculated number of additional miles he would run must not exceed 8 miles

The following are symbols for inequalities and their corresponding meanings:

The inequality format that expresses the information in the question is as follows:

Tom's minimum required running distance must be greater than or equal to the sum of the distance he has already run and the distance he plans to run.

Using this inequality, we can derive the equation

30 ≥ 22 + t

Where t represents the distance Tom plans to run.

To determine the value of t, we must simplify the equation by combining similar terms.

We can subtract 22 from both sides, resulting in

8 ≥ t.

Therefore, the maximum distance Tom plans to run is 8 miles.

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The value of the variable x given the perimeter is 44°.

A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends. A slice of pizza or a pie can be used as an analogy for the form of a circle's sector.

Given: radius = 24cm

perimeter (total) of sector = 68cm

Total perimeter of sector=68cm

Radius = 24 cm

24 + x = 68 cm

x =68 - 24

x = 44°

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A diagram shows a sector of a circle of radius 24 cm and perimeter of 68cm. Find the value of x.

The axis of rotation is a perpendicular line that passes through the vertex, meaning the lowest point in the graph [tex](4, -3)[/tex].

A vertices is a place on a polygons where two ray or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices. For instance, the lines A, B, C, E, etc E in the aforementioned figures are vertices.

A node of a graph, or one of the vertices from which a graph is formed and that can be connected by graph, is referred to as a "vertex" in computing. Moreover, the words "point," "junction," and "0-simplex" are employed.

To graph the function [tex]f(x) = x^2 - 8x + 13[/tex], we need to find its axis of symmetry, vertex, and a few other points.

Find the axis of symmetry

[tex]x = -b/2a[/tex]

In this case, [tex]a = 1[/tex] and [tex]b = -8[/tex], so the axis of symmetry is [tex]x = -(-8)/(2*1) = 4[/tex].

Find the vertex

[tex]f(4) = 4^2 - 8(4) + 13 = -3[/tex]

So the vertex is [tex](4, -3)[/tex].

To find other points,

When [tex]x = 0, y = 13[/tex]

When [tex]x = 1, y = 6[/tex]

When [tex]x = 2, y = 1[/tex]

When [tex]x = 3, y = -2[/tex]

When [tex]x = 5, y = 2[/tex]

These points cannot be connected on a graph to form a basic picture of the function.

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Answer:

A

Step-by-step explanation:

a. To establish whether the function is concave up or concave down, we must obtain the function's second derivative. F(x) = 2x2 - 12x + 9 F'(x) = 4x - 12 F"(x) = 4x - 12 F"(x) = 4.

The function is concave up because the second derivative has a constant value of 4, which is positive. Since the coefficient of x2 is more than one, the function is narrower than the conventional parabola y = x2. b. The equation x = -b/2a gives the parabola's axis of symmetry, where a and b are the coefficients of the x2 and x terms, respectively.A = 2 and b = -12 for the function F(x) = 2x2 - 12x + 9. As a result, the axis of symmetry is x = -12/(2*2) = 3. c. The point at which The coordinates (h, k) define the parabola, where h = -b/2a and k = f. (h). We already determined that the axis of symmetry for the function F(x) = 2x2 - 12x + 9 is x = 3. So, h = 3. To find k, enter h = 3 into the function: F(3) = 2(3)^2 - 12(3) + 9 = -9 As a result, the vertex is (3, -9). Width: The parabola's width is the distance between the x-intercepts, which may be calculated using the quadratic formula.

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According the given question 0.0939 as a Fraction equals 939/10000.

Fractiοns are referred tο as a whοle's cοnstituent parts in mathematics. A single item οr a cοllectiοn οf items can be the cοmplete. When we really cut a slice οf cake frοm the cοmplete cake, the cοmpοnent represents the percentage οf the cake. The wοrd "fractiοn" cοmes frοm Latin.

To write 0.09390 as a fraction you have to write .09390 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.

.09390 = .09390/1 = 0.939/10 = 9.39/100 = 93.9/1000 = 939/10000

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Complete Question:

Express 0.09390.0939 as a fraction.

The total number of voters in favor of Bond Measure A is 3900 voters in favor of Bond Measure A.

First we need to calculate the total number of voters who are registered Democrats and the total number of voters who are not registered Democrats, and then calculate the number of voters in favor of the measure for each group and add them together.

Total number of registered Democrats:

3/4 of 6000 registered voters = 4500 registered Democrats

Number of registered Democrats in favor of Bond Measure A:

2/3 of 4500 registered Democrats = 3000 registered Democrats in favor of the measure

Number of registered Democrats not in favor of Bond Measure A:

4500 - 3000 = 1500 registered Democrats not in favor of the measure

Total number of voters who are not registered Democrats:

6000 - 4500 = 1500 voters who are not registered Democrats

Number of voters who are not registered Democrats and in favor of Bond Measure A:

3/5 of 1500 voters who are not registered Democrats = 900 voters who are not registered Democrats and in favor of the measure

Therefore, the total number of voters in favor of Bond Measure A is:

3000 registered Democrats in favor + 900 other registered voters in favor = 3900 voters in favor of Bond Measure A.

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m is parallel to AB, and passing through points C.

Therefore, m II AB.

In geometry, a line segment is a part of a line bounded by two distinct endpoints and contains every point of the line between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed segment includes two endpoints, an open segment does not include both endpoints; a half-open segment has exactly one end. In geometry, a line segment is usually represented using a line above the two end symbols (like AB).

We use the basic rules of construction to draw lines according to the problem.

Draw a straight line AB and take a point C outside of it. Using a ruler and compass to draw the AB line, follow the steps below:

Therefore, the line l is parallel to the line AB.

Complete Question:

Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.

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The rate of change and initial value are 0.023 and -600 respectively.

The amount he needs to sell to break even is $26,086.96.

The amount he needs to sell in order to make $1000 profit is $69,565.22.

Mathematically, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided, a system of equations that models the situation is given by;

-140 = 20,000x + c    ...equation 1.

90 = 10,000x + c       ...equation 2.

By subtracting equation 1 from equation 2, we have:

230 = 10,000x

x = 0.023

For the initial value, we have:

90 = 10,000x + c

c = -140 - 20,000(0.023)

c = -600.

In order to break even, y must be equal to 0;

y = 0.023x - 600

0 = 0.023x - 600

x = 600/0.023

x = $26,086.96.

In order to make $1000 profit, Lanny must sell the following:

y = 0.023x - 600

1,000 = 0.023x - 600

x = 400/0.023

x = $69,565.22.

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Answer:

Step-by-step explanation:

-10 perecent

because 21-11=10

The graphs of f of x equals cosine of the quantity x over 2 and g of x equals square root of 3 minus cosine of the quantity x over 2 intersect on the interval [0, 360°) at: D. 30° and 330°.

In Mathematics and Geometry, a point of intersection simply refers to the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

In this context, we can logically deduce that the point of intersection of the graphs would be at function f(x) = function g(x):

[tex]cos(\frac{x}{2} )=\sqrt{3} -cos(\frac{x}{2} )\\\\\sqrt{3}=cos(\frac{x}{2} ) + cos(\frac{x}{2} )\\\\\sqrt{3}=2cos(\frac{x}{2} )\\\\cos(\frac{x}{2} )=\frac{\sqrt{3}}{2} \\\\cos(\frac{x}{2} )=\frac{\sqrt{3}}{2}\times \frac{\sqrt{3}}{\sqrt{3}} \\\\cos(\frac{x}{2} )= \frac{3}{2\sqrt{3}}[/tex]

x/2 = 15

x = 15(2)

x = 30

x/2 = 165

x = 2(165)

x = 330.

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The optimal solution of an objective function does not change when its coefficients are changed within a certain range of values. This range of values for each coefficient depends on the function itself and the value of other coefficients.

For example, if the objective function is 3x + 2y, then the range of values for the coefficient of x (3) can be changed from 2 to 4 without changing the optimal solution. Similarly, the coefficient of y (2) can be changed from 1 to 3 without changing the optimal solution.
Therefore, the ranges of values for each coefficient of the objective function, holding all else constant, can be changed without changing the optimal solution.

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Answer:

The answer to your problem is, 156

First lets find out how many feet or in one yard ?

Well 1 yard = 3 feet.

Now that we know that we can use our knowledge to answer the next question:

If Bill ran 52 yards, how many feet did he ran?

We can do math to solve our answer. :

1 x 52 = 52.

Now we need to multiply 52 x 3.

That is a little bit to much, so lets make the problem easier!

By breaking up the problem \/ to make it more easier.

50 x 3. ( 5 x 3 = 15, just add a zero! ) = 150

3 x 2 = 6.

Next add:

150 + 6 = 156.

Thus the answer to your problem is, 156

[tex](\stackrel{x_1}{1}~,~\stackrel{y_1}{-3})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{(-3)}}}{\underset{\textit{\large run}} {\underset{x_2}{3}-\underset{x_1}{1}}} \implies \cfrac{-4 +3}{2} \implies \cfrac{ -1 }{ 2 } \implies - \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{1}) \implies y +3 = - \cfrac{ 1 }{ 2 } ( x -1) \\\\\\ y+3=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}\implies y=- \cfrac{ 1 }{ 2 }x+\cfrac{1}{2}-3\implies {\Large \begin{array}{llll} y=- \cfrac{ 1 }{ 2 }x-\cfrac{5}{2} \end{array}}[/tex]

Answer: First, let's find the slope of the line:

slope = (change in y) / (change in x)

slope = (-4 - (-3)) / (3 - 1)

slope = -1/2

Now, let's choose one of the points, say (1,-3), and use the point-slope formula:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) are the coordinates of the point.

So, substituting in the values we get:

y - (-3) = (-1/2)(x - 1)

Simplifying this equation, we get:

y + 3 = (-1/2)x + 1/2

Subtracting 3 from both sides, we get:

y = (-1/2)x - 5/2

Therefore, the equation of the line that passes through the points (1,-3) and (3,-4) is y = (-1/2)x - 5/2.

Your welcome.

Step-by-step explanation:

The standard pyramid KO has a volume of roughly 64.88 cubic units.

To find the volume of the given regular pyramid KO, we need to know the area of the base and the height of the pyramid. Since the pyramid is regular, the base is a square. Let the side of the square base be x.

Now, we can use trigonometry to find the height of the pyramid. Draw a line from vertex K to the center O of the base. This line is perpendicular to the base, so it splits the base into two equal parts. Let M be the midpoint of side AB. Then, we have right triangle KMO with hypotenuse KO, and angle MKO equal to half of angle AKO (19 degrees).

We can use the trigonometric function tangent to find the height h of the pyramid:

tan 19 = h/5 (where 5 is half of x, the side length of the base)

h = 5 tan 19 ≈ 1.98

Now, we can use the formula for the volume of a pyramid:

V = (1/3) * area of base * height

Since the base is a square, its area is x². Substituting the known values, we get:

V = (1/3) * x² * h

V = (1/3) * x² * 1.98

V = (0.66) x²

We are given that KO = 10.2, which is the slant height of the pyramid. Using the Pythagorean theorem, we can find x:

x² + (5/2)² = 10.2²

x² = 104.04 - 6.25

x² = 97.79

x ≈ 9.89

Substituting this value for x into the equation for the volume, we get:

V = (0.66) * 9.89²

V ≈ 64.88

Therefore, the volume of the regular pyramid KO is approximately 64.88 cubic units.

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V = π(√(803.84/π))^2(12.25) = 9587.15 ft^3. Hence, following Cavalieri's theory, the solid cylinder has a volume of around 9587.15 ft3.

According to Cavalieri's principle, if two solids have the same height and every plane section passing through one solid along the height has the same area as the corresponding plane section passing through the other solid, the two solids must also have the same volume.

A circle of radius r has the same cross-section as a solid cylinder. A = r2 calculates the circle's area.

Therefore, πr^2 = 803.84 r^2 = 803.84/π\sr = √(803.84/π)

The solid cylinder is 12.25 feet tall.

We may get the volume of the solid cylinder using the volume of a cylinder formula, V = r2h: V = π(√(803.84/π))^2(12.25) = 9587.15 ft^3

Hence, following Cavalieri's theory, the solid cylinder has a volume of around 9587.15 ft3.

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The standard error of the distribution of sample proportions is approximately 0.090.

The formula to find the standard error of the distribution of sample proportions is given by:Standard error = √(p(1-p)/n)Where,p = Sample proportionn = Sample sizeGiven that the sample proportion is 0.450 and the sample size is 31, we can substitute the values into the formula to find the standard error.Standard error = √(0.450(1-0.450)/31) ≈ 0.090So, the standard error of the distribution of sample proportions is approximately 0.090.

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Answer:

Step-by-step explanation:

To solve the system of equations algebraically, we need to substitute the second equation into the first equation and solve for x:

y = 4x – 5 (equation 1)

y = -3 (equation 2)

Substitute equation 2 into equation 1:

-3 = 4x – 5

Add 5 to both sides:

2 = 4x

Divide both sides by 4:

x = 1/2

Now, we can substitute this value of x back into either equation to find y:

y = 4(1/2) – 5 = -3

Therefore, the solution to the system of equations is (1/2, -3).

To verify this solution using the graph, we can plot the two equations on the same set of axes:

y = 4x – 5 (red line)

y = -3 (blue line)

The two lines intersect at the point (1/2, -3), confirming our solution.

Therefore, the answer is (B) (1/2, -3).

 This function is neither odd nor even. To show this, we can take the algebraic approach.

The definition of an odd function is that for every \( x \), \( f(-x) = -f(x) \).

Therefore, we can substitute \( -x \) for \( x \) and see if this statement is true.

\( f(-x) = 6(-x)^{2}-\frac{4}{-x} \)

\( f(-x) = -6 x^{2}+\frac{4}{x} \)

Since this is not equal to \( -f(x) \), which is \( -6 x^{2}-\frac{4}{x} \), this function is neither odd nor even.

9) The equation of the line that goes through the two points \( (-1,3) \) and \( (2,-4) \) is \( y = \frac{1}{3}x + \frac{17}{3} \).

To find the equation, we can use the point-slope formula. The slope of the line is \( \frac{-7}{3} \), which we can find using the two points.

\( m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{-4-3}{2-(-1)} = \frac{-7}{3} \)

The point-slope formula for the equation of the line is \( y - y_{1} = m(x - x_{1}) \). We can substitute in the slope and the point \( (-1,3) \) to get the equation.

\( y - 3 = \frac{-7}{3}(x - (-1)) \)

\( y - 3 = \frac{-7}{3}(x + 1) \)

\( y = \frac{-7}{3}x - \frac{7}{3} + 3 \)

\( y = \frac{1}{3}x + \frac{17}{3} \)

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To classify a quadrilateral by its most specific name, we need to examine its sides and angles.

A quadrilateral is four-sided polygon with four angles. It is closed shape with straight lines that do not cross each other.

Here are the most common types of quadrilaterals and their defining characteristics:

Parallelogram - quadrilateral consist of two pairs of parallel sides.

Rectangle - parallelogram with four right angles.

Rhombus -  parallelogram with four congruent sides.

Square - rectangle and a rhombus, with four right angles and four congruent sides.

Let's consider an example.Suppose we are given a quadrilateral with four sides of equal length and two pairs of opposite parallel sides. This means that it has the characteristics of a parallelogram and a rhombus.

Reasoning: The quadrilateral has four equal sides, which makes it a rhombus. Additionally, it has two pairs of parallel sides, which satisfies the criteria for a parallelogram. However, since a rhombus is a type of parallelogram with additional properties, it is the most specific name for this quadrilateral.

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It would take them about 8.4 hours to add the special effects if they all work together.

1/T = 1/T1 + 1/T2 + 1/T3 +... + 1/Tn, where T is the time it takes for all n persons to complete the task and T1, T2,..., Tn are the times it takes for each person to do the task individually, is the formula for addressing issues involving work done by several people. This equation is based on the premise that each person's contribution to the activity is inversely proportionate to the time it takes them to do it. In other words, a person contributes more effort to the entire task the faster they work. This method may be used to determine how long it will take all n persons working together to do the assignment in total.

The work done is calculated by:

1/T = 1/T1 + 1/T2 + 1/T3

Here, we have T1 = 20, T2 = 26 and T3 = 32 hours for work done separately.

Substituting the values:

1/T = 1/20 + 1/26 + 1/32

1/T = (32/640) + (24/640) + (20/640)

1/T = 76/640

T = 640/76

T ≈ 8.4 hours

Therefore, it would take them about 8.4 hours to add the special effects if they all work together.

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Answer:

This function has no zeroes

Step-by-step explanation:

To understand this problem we need to first understand what the zeroes of a function is; the zeroes of a function is the point at which the y value of a solution is equal to zero. So in this scenario all we need to do is plug 0 in for y:

[tex]0 = x^2 +49[/tex]

Subtract 49 from both sides:

[tex]-49 = x^2[/tex]

Now we can notice that [tex]x^2[/tex] is equal to -49; to our surprise there is no possible value for [tex]x^2[/tex] to be equal to a negative number. Therefore this function has no roots.

Step-by-step explanation:

a zero of a function means what value of x causes a functional value of 0 ?

so,

0 = x² + 49

-49 = x²

x = ±sqrt(-49)

this tells us that there is no solution in real numbers, because no square of any real number can be negative.

but the function still has 2 zeroes. they are numbers of the set of imaginary or complex numbers.

that means they base on the square root of -1, called i.

x = ±sqrt(49×-1) = ±7×sqrt(-1) = ±7i

Answer:

m = -1

Step-by-step explanation:

Let's change the equation to y = mx + b

m = the slope

x + y = 9

Subtract x both sides

y = -x + 9

m = -1

So, the slope is -1

The given expression can be simplified to x2 - xy = 3.

Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.

This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as x2 - xy = 3.

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The given expression can be simplified to 25 + 5y + 4.

Expression is a way to communicate ideas, feelings, and thoughts. It can be verbal, physical, and/or written. Expression is the outward manifestation of your inner emotions, which can take many forms. Expression can be used to express joy, sadness, anger, and other emotion. It can also be used to articulate a point of view or opinion. Expression is an important part of communication and is a powerful tool to express oneself and one’s feelings.

To simplify the expression x + 8 and = 3, we must first subtract 8 from both sides of the equation to get x = -5. We can then substitute -5 for x in the expression x2 - xy + 4, resulting in (-5)2 - (-5)y + 4.

Simplifying further, we get 25 - (-5)y + 4, or 25 + 5y + 4. Therefore, the simplified expression is 25 + 5y + 4.


This is happening because the addition of 8 to x can be rewritten as x2, and the equal sign can be used to indicate that the two sides of the equation must be equal. Therefore, both sides can be simplified to their original terms. Thus, the expression can be written as 25 + 5y + 4.

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Answer:

[tex]a_{n}[/tex] = 3 + 5(n - 1)

Step-by-step explanation:

there is a common difference between consecutive terms , that is

8 - 3 = 13 - 8 = 18 - 13 = 5

this indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 3 and d = 5 , then

[tex]a_{n}[/tex] = 3 + 5(n - 1) ← is the explicit formula

Answer:

(x+5)^2 + (y+12)^2 = 49

Step-by-step explanation:

(x-h)^2 + (y-k)^2 = r ^2 is the general equation for circles, where r is the radius and h,k are the center's coordinates.

(a) Compared to the graph of y = x, the graph of y = x - 4 is shifted downwards by 4 units.

Compared to the graph of y = x, the graph of y = x - 4 intersects the y-axis at the point (0, -4).

(b) Compared to the graph of y = x, the graph of y = 5/2 * x is steeper (has a greater slope).

Compared to the graph of y = x, the graph of y = 5/2 * x intersects the y-axis at the point (0, 0).

(a)

Compared to the graph of y = x, the graph of y = x - 4 is shifted downwards by 4 units. The -4 in the second equation means shifting downward 4 units

Compared to the graph of y = x, the graph of y = x - 4 intersects the y-axis at the point (0, -4). hence the y intercept is -4

(b)

Compared to the graph of y = x, the graph of y = 5/2 * x is steeper (has a greater slope).

Compared to the graph of y = x, the graph of y = 5/2 * x intersects the y-axis at the point (0, 0). In this case both graphs intercepts the y-axis at same point which is at the origin

The graphs are attached

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The percentage decrease in the price of the microwave is 51.82%.

Percentage is used to determine the relative value of a digit as a number out of a hundred. The sign that is used to represent percentages is %. In order to express a value as a percentage, multiply the number by 100. Percentage is a measure of frequency.

Percentage decrease = (change in price / initial price) x 100

Change in price = initial price - new price

$137 - $66 = $71

(71/137) x 100 = 51.82%

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Step-by-step explanation:

Let the coordinates of the left endpoint of the line segment be (x1, y1) and the coordinates of the right endpoint be (x2, y2). Let the point dividing the line segment be (x, y). Then the distance between the left endpoint and (x, y) is mx/(m+n) and the distance between (x, y) and the right endpoint is nx/(m+n).

Using the distance formula, we have:

[tex]distance \: between \: (x1, y1) \: and \: (x, y) = \sqrt{((x - x1)^2 + (y - y1)^2)} = \frac{mx}{(m+n)} [/tex]

[tex]distance \: between \: (x, y) \: and \: (x2, y2) = \sqrt{((x2 - x)^2 + (y2 - y)^2)} = \frac{nx}{(m+n)} [/tex]

Squaring both equations, we get:

[tex](x - x1)^2 + (y - y1)^2 = \frac{mx}{(m+n)^2}[/tex]

[tex](x2 - x)^2 + (y2 - y)^2 = \frac{nx}{(m+n)^2}[/tex]

Expanding the squares, we get:

[tex]x^2 - 2x1x + x1^2 + y^2 - 2y1y + y1^2 = \frac{mx}{(m+n)^2} [/tex]

[tex]x^2 - 2x2x + x2^2 + y^2 - 2y2y + y2^2 = \frac{nx}{(m+n)^2}[/tex]

Rearranging and simplifying, we get:

[tex]x = \frac{(mx2 + nx1)}{(m+n)} \: and \: y = \frac{(my2 + ny1)}{(m+n)}[/tex]

Therefore, the point that divides the line segment into two parts so that the ratio of the lengths is m: n and the point is closer to the left endpoint is:

[tex](x, y) = \frac{(mx2 + nx1)}{(m+n)}, \frac{(my2 + ny1)}{(m+n)}[/tex]